cp's OEIS Frontend

A241093 Number of partitions p of n into distinct parts such that max(p) > 1 + 2*(number of parts of p).

%I A241093 #10 Nov 09 2024 02:28:48
%S A241093 0,0,0,0,1,1,1,2,3,4,5,7,8,11,13,17,21,26,31,38,45,54,65,77,92,108,
%T A241093 128,149,175,203,237,274,318,366,424,486,559,640,733,836,953,1084,
%U A241093 1232,1398,1583,1792,2025,2286,2576,2902,3262,3666,4111,4610,5160,5774
%N A241093 Number of partitions p of n into distinct parts such that max(p) > 1 + 2*(number of parts of p).
%F A241093 a(n) + A241086(n) + A241093(n) = A000009(n) for n >= 1.
%e A241093 a(12) counts these 8 partitions: {12}, {11,1}, {10,2}, {9,3}, {9,2,1}, {8,4}, {8,3,1}, {7,5}.
%t A241093 z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t A241093 Table[Count[f[n], p_ /; Max[p] < 1 + 2*Length[p]], {n, 0, z}] (*A241086*)
%t A241093 Table[Count[f[n], p_ /; Max[p] <= 1 + 2*Length[p]], {n, 0, z}](*A241091*)
%t A241093 Table[Count[f[n], p_ /; Max[p] == 1 + 2*Length[p]], {n, 0, z}](*A241092*)
%t A241093 Table[Count[f[n], p_ /; Max[p] >= 1 + 2*Length[p]], {n, 0, z}](*A241089*)
%t A241093 Table[Count[f[n], p_ /; Max[p] > 1 + 2*Length[p]], {n, 0, z}] (*A241093*)
%Y A241093     Cf. A241086, A241091, A241092, A000009.
%K A241093 nonn,easy
%O A241093 0,8
%A A241093 _Clark Kimberling_, Apr 18 2014